Oscillating path between self-similarities in liquid pinch-off.

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Mathematical physics

Background:

• Singular behaviors in differential equations are common in natural sciences.
• Self-similar solutions can describe evolving singularities, but regime transitions are poorly understood.

Purpose of the Study:

• To investigate the transition between self-similar regimes in a viscous liquid thread pinch-off.
• To understand the role of system geometry and external perturbations in this transition.

Main Methods:

• Experimental study of viscous liquid thread pinch-off.
• Analysis of symmetric and asymmetric solutions.
• Observation of transient regimes and oscillations.

Main Results:

• System geometry and external perturbations are crucial for transitioning from symmetric to asymmetric solutions.
• The transient regime exhibits unexpected log-scale oscillations.
• These oscillations significantly delay the onset of the final self-similar solution.

Conclusions:

• External constraints strongly influence predictions for phenomena like satellite droplet formation.
• Understanding these transitions is vital for accurate rheological testing and fluid behavior modeling.